Magma V2.20-10 Tue Mar 3 2015 21:01:28 on mathcompprd01 [Seed = 3964572440] Type ? for help. Type -D to quit. Loading startup file "/home/eobr007/.magma.startup" Loading "sign.m" > > n := 6; > G := PermutationGroup ("3A6", 1); > p := 5; > L := IrreducibleModules (G, GF(p)); > L := [ActionGroup (x): x in L]; > L := [x : x in L | #x eq #G and Degree (x) eq 6]; > "Degrees of faithful repns are ", [Degree (x): x in L]; Degrees of faithful repns are [ 6 ] > f := ProcessReps (L, n); Consider the following repn 1 Input degree = 6 Defining field size = 5 Order of generators [ 2, 4, 4, 2 ] Composition Factors of G is G | Alternating(6) * | Cyclic(3) * | Cyclic(2) * | Cyclic(2) 1 Refined bound on degree is 7 Order of G is 4320 ... #O is now 432 ... #O is now 1512 ... #O is now 3672 ... #O is now 5832 ... #O is now 7992 ... #O is now 10152 ... #O is now 10872 ... #O is now 11592 Proved no regular orbit ======================================== Input degree = 6 Defining field size = 5 Order of generators [ 2, 4, 2 ] Composition Factors of G is G | Alternating(6) * | Cyclic(3) * | Cyclic(2) 1 Refined bound on degree is 7 Order of G is 2160 ... #O is now 1080 ... #O is now 2160 ... #O is now 3240 ... #O is now 4320 ... #O is now 4680 ... #O is now 5760 ... #O is now 6120 ... #O is now 7200 ... #O is now 8280 ... #O is now 9360 ... #O is now 9720 ... #O is now 10800 ... #O is now 11016 ... #O is now 11286 ... #O is now 11646 ... #O is now 11862 ... #O is now 12942 ... #O is now 13212 ... #O is now 13572 Proved no regular orbit ======================================== Input degree = 6 Defining field size = 5 Order of generators [ 2, 4 ] Composition Factors of G is G | Alternating(6) * | Cyclic(3) 1 Refined bound on degree is 6 Order of G is 1080 Found regular orbit ======================================== > > n := 7; > G := PermutationGroup ("3A7", 1); > p := 5; > L := IrreducibleModules (G, GF(p)); > L := [ActionGroup (x): x in L]; > L := [x : x in L | #x eq #G and Degree (x) eq 6]; > "Degrees of faithful repns are ", [Degree (x): x in L]; Degrees of faithful repns are [ 6 ] > f := ProcessReps (L, n); Consider the following repn 1 Input degree = 6 Defining field size = 5 Order of generators [ 3, 5, 4, 2 ] Composition Factors of G is G | Alternating(7) * | Cyclic(3) * | Cyclic(2) * | Cyclic(2) 1 Vector space too small -- no regular orbit ======================================== Input degree = 6 Defining field size = 5 Order of generators [ 3, 5, 2 ] Composition Factors of G is G | Alternating(7) * | Cyclic(3) * | Cyclic(2) 1 Refined bound on degree is 8 Order of G is 15120 ... #O is now 630 Proved no regular orbit ======================================== Input degree = 6 Defining field size = 5 Order of generators [ 3, 5 ] Composition Factors of G is G | Alternating(7) * | Cyclic(3) 1 Refined bound on degree is 7 Order of G is 7560 ... #O is now 2520 ... #O is now 5040 ... #O is now 5670 ... #O is now 7182 ... #O is now 7812 ... #O is now 9324 Proved no regular orbit ======================================== > > n := 6; > G := PermutationGroup ("3S6", 1); > p := 5; > L := IrreducibleModules (G, GF(p)); > L := [ActionGroup (x): x in L]; > L := [x : x in L | #x eq #G and Degree (x) eq 6]; > "Degrees of faithful repns are ", [Degree (x): x in L]; Degrees of faithful repns are [ 6 ] > f := ProcessReps (L, n); Consider the following repn 1 Input degree = 6 Defining field size = 5 Order of generators [ 2, 5, 4, 2 ] Composition Factors of G is G | Cyclic(2) * | Alternating(6) * | Cyclic(3) * | Cyclic(2) * | Cyclic(2) 1 Refined bound on degree is 7 Order of G is 8640 ... #O is now 4320 ... #O is now 4752 ... #O is now 5292 ... #O is now 5832 ... #O is now 6264 ... #O is now 10584 Proved no regular orbit ======================================== Input degree = 6 Defining field size = 5 Order of generators [ 2, 5, 2 ] Composition Factors of G is G | Cyclic(2) * | Alternating(6) * | Cyclic(3) * | Cyclic(2) 1 Refined bound on degree is 7 Order of G is 4320 ... #O is now 1080 ... #O is now 3240 ... #O is now 5400 ... #O is now 5760 ... #O is now 6120 ... #O is now 8280 ... #O is now 9360 ... #O is now 9720 ... #O is now 11880 Proved no regular orbit ======================================== Input degree = 6 Defining field size = 5 Order of generators [ 2, 5 ] Composition Factors of G is G | Cyclic(2) * | Alternating(6) * | Cyclic(3) 1 Refined bound on degree is 7 Order of G is 2160 ... #O is now 1080 Found regular orbit ======================================== > > n := 7; > > G := PermutationGroup ("3S7", 1); > p := 5; > L := IrreducibleModules (G, GF(p)); > L := [ActionGroup (x): x in L]; > L := [x : x in L | #x eq #G and Degree (x) eq 6]; > "Degrees of faithful repns are ", [Degree (x): x in L]; Degrees of faithful repns are [ 6 ] > f := ProcessReps (L, n); Consider the following repn 1 Input degree = 6 Defining field size = 5 Order of generators [ 2, 6, 4, 2 ] Composition Factors of G is G | Cyclic(2) * | Alternating(7) * | Cyclic(3) * | Cyclic(2) * | Cyclic(2) 1 Vector space too small -- no regular orbit ======================================== Input degree = 6 Defining field size = 5 Order of generators [ 2, 6, 2 ] Composition Factors of G is G | Cyclic(2) * | Alternating(7) * | Cyclic(3) * | Cyclic(2) 1 Vector space too small -- no regular orbit ======================================== Input degree = 6 Defining field size = 5 Order of generators [ 2, 6 ] Composition Factors of G is G | Cyclic(2) * | Alternating(7) * | Cyclic(3) 1 Refined bound on degree is 8 Order of G is 15120 ... #O is now 1512 Proved no regular orbit ======================================== > > G := PermutationGroup ("3A7", 1); > p := 7; > L := IrreducibleModules (G, GF(p)); > L := [ActionGroup (x): x in L]; > L := [x : x in L | #x eq #G and Degree (x) eq 6]; > "Degrees of faithful repns are ", [Degree (x): x in L]; Degrees of faithful repns are [ 6, 6 ] > f := ProcessReps (L, n); Consider the following repn 1 Input degree = 6 Defining field size = 7 Order of generators [ 3, 5, 2 ] Composition Factors of G is G | Alternating(7) * | Cyclic(3) * | Cyclic(2) 1 Refined bound on degree is 7 Order of G is 15120 ... #O is now 7560 ... #O is now 15120 ... #O is now 18900 ... #O is now 22680 ... #O is now 24570 ... #O is now 27090 ... #O is now 34650 ... #O is now 42210 ... #O is now 49770 ... #O is now 52290 ... #O is now 54810 ... #O is now 62370 ... #O is now 69930 ... #O is now 71820 ... #O is now 79380 ... #O is now 80640 ... #O is now 88200 ... #O is now 91980 ... #O is now 94500 ... #O is now 98280 ... #O is now 100170 ... #O is now 103950 Proved no regular orbit ======================================== Input degree = 6 Defining field size = 7 Order of generators [ 3, 5 ] Composition Factors of G is G | Alternating(7) * | Cyclic(3) 1 Refined bound on degree is 7 Order of G is 7560 ... #O is now 3780 ... #O is now 7560 ... #O is now 9450 ... #O is now 10710 ... #O is now 11340 ... #O is now 12285 ... #O is now 13545 ... #O is now 17325 ... #O is now 21105 ... #O is now 24885 ... #O is now 28665 ... #O is now 32445 ... #O is now 33075 ... #O is now 36855 ... #O is now 40635 ... #O is now 44415 ... #O is now 45360 ... #O is now 49140 ... #O is now 51030 ... #O is now 54810 ... #O is now 58590 ... #O is now 62370 ... #O is now 63315 ... #O is now 63945 ... #O is now 64890 ... #O is now 68670 ... #O is now 70560 ... #O is now 72450 ... #O is now 76230 ... #O is now 76860 ... #O is now 80640 ... #O is now 81396 ... #O is now 82656 ... #O is now 86436 ... #O is now 88326 ... #O is now 89082 ... #O is now 90027 ... #O is now 90972 ... #O is now 91917 ... #O is now 95697 ... #O is now 96957 ... #O is now 98217 ... #O is now 100107 ... #O is now 103887 ... #O is now 105147 ... #O is now 106407 ... #O is now 107163 ... #O is now 109053 ... #O is now 109998 ... #O is now 110628 Proved no regular orbit ======================================== Consider the following repn 2 Input degree = 6 Defining field size = 7 Order of generators [ 3, 5, 2 ] Composition Factors of G is G | Alternating(7) * | Cyclic(3) * | Cyclic(2) 1 Refined bound on degree is 7 Order of G is 15120 ... #O is now 7560 ... #O is now 15120 ... #O is now 17640 ... #O is now 25200 ... #O is now 28980 ... #O is now 32760 ... #O is now 34650 ... #O is now 42210 ... #O is now 49770 ... #O is now 57330 ... #O is now 64890 ... #O is now 68670 ... #O is now 70182 ... #O is now 73962 ... #O is now 75852 ... #O is now 83412 ... #O is now 85302 ... #O is now 86562 ... #O is now 88452 ... #O is now 92232 ... #O is now 94752 ... #O is now 97272 ... #O is now 97398 ... #O is now 98028 ... #O is now 105588 Proved no regular orbit ======================================== Input degree = 6 Defining field size = 7 Order of generators [ 3, 5 ] Composition Factors of G is G | Alternating(7) * | Cyclic(3) 1 Refined bound on degree is 7 Order of G is 7560 ... #O is now 3780 ... #O is now 7560 ... #O is now 8820 ... #O is now 12600 ... #O is now 16380 ... #O is now 20160 ... #O is now 21420 ... #O is now 22176 ... #O is now 22302 ... #O is now 23562 ... #O is now 25452 ... #O is now 27342 ... #O is now 28287 ... #O is now 30177 ... #O is now 33957 ... #O is now 37737 ... #O is now 41517 ... #O is now 45297 ... #O is now 49077 ... #O is now 49392 ... #O is now 50652 ... #O is now 54432 ... #O is now 58212 ... #O is now 58968 ... #O is now 62748 ... #O is now 66528 ... #O is now 70308 ... #O is now 71064 ... #O is now 74844 ... #O is now 78624 ... #O is now 79884 ... #O is now 80829 ... #O is now 84609 ... #O is now 85239 ... #O is now 89019 ... #O is now 89649 ... #O is now 90909 ... #O is now 92169 ... #O is now 95949 ... #O is now 96894 ... #O is now 98784 ... #O is now 100044 ... #O is now 100800 ... #O is now 102690 ... #O is now 103950 ... #O is now 104580 ... #O is now 106470 ... #O is now 107100 ... #O is now 108990 ... #O is now 109305 ... #O is now 110565 Proved no regular orbit ======================================== > Total time: 4.960 seconds, Total memory usage: 32.09MB